Can a Muslim support gay rights?
Yes. We condone the actions of those who drink alcohol, those who smoke, those who eat pork, those who adulter, those who engage in homosexual acts etc. They are explicitly considered unlawful in Islam.
However nowhere in Islam does it day that we take action directly against these people. We are permitted to express why we believe it's wrong and guide them away from temptation, but simply put we are not allowed to coerce anyone into not doing something. People can act as they wish. We as Muslims for the most part do respect that, seen by the fact that in most western countries we live alongside smokers, drinkers etc. with no issue.
Why should it be any different for people who identify as LGBT?
Most Muslims in the west belive that minorities deserve equal rights (as more often than not we are included in the minortity), but when it comes to this issue, a large number of people either stay silent or go against it.
One thing modern Muslims need to understand is we don't neccesarily need to agree with the actions of people, in order to belive that they deserve the right to carry out those actions. We need to respect the way they choose to live their life. We are free to judge their actions as with anyone, but as people we must judge them with respect and dignity.
What Muslims and non-Muslims alike need to appreciate is that one can continue to think that homosexulaity is unnatural, but simultenously maintain a belief that LGBT people are free to act as they wish. Smoking is technically also unatural, but I believe people should be free to smoke if they so wish.
One belief all Muslims no matter what sect hold true is the fact the only one who can pass judgement is Allah. I don't understand why we seem to disregard this fact and judge people, not just based on their sexuality, but their beliefs and their actions, and in some instances we don't just refuse people of the rights they deserve, we kill them for who they are and what they believe in.
We masquerade behind the false pretence that it is our own religion which gives us reasoning for these beliefs inciting hatred and violence when in reality it's just our ignorant belief in flawed interpretations. Of the various aspects of my religion I learned about while growing up, one that I believe is fundamental is that you do not judge a good-willed person just because they may sin, and under no circumstances do you harm innocent people.
I support gay rights, because I belive in equal rights for all. If a person wishes to act in a way we deem peculiar, who are we to judge?